I do both, TIG brazing (with silicone bronze rod only, I wish I could get some of that aluminium bronze here...) and oxy-fuel brazing. The difference is indeed like night and day.
However, both methods have their strengths and weaknesses. TIG doesn't wet at at all for me. When it melts it almost doesn't flow. It seems a lot more viscous than steel. But it can be pushed with a rod. It is fairly easy to TIG braze on top of a corner, or near a slope where with oxy-fuel braze would just run down. In general I use TIG for 99% of stuff. Only when large surfaces are to be joined and one needs to have the joint wet in between I'd use oxy-fuel.
Also, when I'm TIG brazing cast iron I use AC TIG. On clean steel DC.